So I ran into the old plugged in, not charging problem with my laptop about a month back. I hoped it was the charger, but upon getting a replacement 65-watt charger, the problem persisted. I assumed the fiddly bits on the inside of the laptop had given up the ghost, as I've had that issue before, but when a friend plugged in his 90-watt dell charger it worked like a charm. I'd rather not have to go buy a new 90-watt charger, but I will if I have to.
Also, I suppose I should mention that I'm using a 5759 with no modifications. Also, I used to get an error message every time I plugged in a 65-watt charger though it doesn't show up anymore for whatever reason and I can't remember exactly what it said. Something about it not being recognized or somesuch. Same error message with 3 different 65-watt chargers.